In a certain small town, 3 professional burglars are currently out of prison: Alex, Becky, and Carl. Alex has in the past committed 55% of the burglaries committed by the three, Becky 31%, and Carl the rest. But only 1/3 of Alex’s jobs are burglaries of a residence, while half of Becky’s are, and all of Carl’s are.
a. What is the probability that the next burglary in town (if one of the three did it) is the burglary of a residence?
b. Sure enough, a resident reports a home burglary. If one of the three did it, what is the probability Becky was guilty?
